Christmas Confusion
by Peter Jägare
First, we simplify and number the statements.
A1: water colours to Chester
A2: ribbon to Alice
A3: model train from Deirdre
A4: diary from Alice
A5: diary and pocket watch to Deirdre
A6: loudspeakers from Chester to Bruno
A7: textbook from Bruno
A8: pocket knife not from Chester
B1: DVD player to Alice
B2: textbook to Chester
B3: diary and chocolates to Bruno
B4: chocolates from Alice
B5: socks from Bruno
B6: DVD player from Bruno
B7: model train from Bruno
B8: mittens from Alice to Bruno
C1: pocket watch to Bruno
C2: ribbon to Bruno
C3: DVD player from Chester
C4: pocket watch from Alice
C5: ribbon from Chester
C6: diary from Chester
C7: textbook from Chester
C8: pocket knife from Chester to Deirdre
D1: socks to Alice
D2: loudspeakers to Bruno
D3: DVD player to Deirdre
D4: model train to Bruno
D5: water colours from Deirdre to Chester
D6: chocolates to Chester
D7: pocket watch to Chester
D8: textbook and ribbon to Alice
Figuring out which family member is always correct would be helpful. C3, C5, C6, C7 and C8 together claim that Chester gave five gifts. Since each family member only gave one gift to each of the other family members, Chester is not always correct.
B3 and B4 mean that Alice gave Bruno the box of chocolates, but B8 says her gift to him was the mittens. So Bruno is not always correct.
Let's assume Deirdre is always correct. This gives us the following:
| Alice | Bruno | Chester | Deirdre |
| Alice | ------ | | | |
| Bruno | | ------ | | |
| Chester | | | ------ | |
| Deirdre | | | Water colours | ------ |
| Socks | Loudspeakers | Chocolates | DVD player |
| Textbook | Model train | Pocket watch | |
| Ribbon | | | |
| T | A1: water colours to Chester |
| T | A2: ribbon to Alice |
| | A3: model train from Deirdre |
| | A4: diary from Alice |
| F | A5: diary and pocket watch to Deirdre |
| | A6: loudspeakers from Chester to Bruno |
| | A7: textbook from Bruno |
| | A8: pocket knife not from Chester |
| F | B1: DVD player to Alice |
| F | B2: textbook to Chester |
| F | B3: diary and chocolates to Bruno |
| | B4: chocolates from Alice |
| | B5: socks from Bruno |
| | B6: DVD player from Bruno |
| F | B7: model train from Bruno |
| | B8: mittens from Alice to Bruno |
| F | C1: pocket watch to Bruno |
| F | C2: ribbon to Bruno |
| | C4: pocket watch from Alice |
| | C6: diary from Chester |
At least one of C3 and C8 is false:
| | C3: DVD player from Chester |
| | C8: pocket knife from Chester to Deirdre |
At least one of C5 and C7 is false:
| | C5: ribbon from Chester |
| | C7: textbook from Chester |
| T | D1: socks to Alice |
| T | D2: loudspeakers to Bruno |
| T | D3: DVD player to Deirdre |
| T | D4: model train to Bruno |
| T | D5: water colours from Deirdre to Chester |
| T | D6: chocolates to Chester |
| T | D7: pocket watch to Chester |
| T | D8: textbook and ribbon to Alice |
No contradictions so far. We can concude that Alice has to be the 3/4 correct family member, since Bruno and Chester both have four false statements each. Let's add another assumption: That Bruno is right half the time. That means that B4, B5, B6 and B8 have to be true. B5 means that A7 has to be false (or Bruno gave Alice two presents). Since we now know Alice's two false statements, the remaining one's have to be true.
A4 and A8 mean that C6 and C8 are false. B6 means that C3 is false. B4 means that C4 is false (else Alice gave Chester two presents). But since one of C5 and C7 have to be false (else Chester gives Alice two presents), Chester has at most one true statement, which is less than one quarter.
That's a contradiction, so if Deirdre is always correct, Bruno is only correct one quarter of the time and Chester is correct half the time. Moving back to before we assumed Bruno to be correct half the time, this means that C4 and C6 are true. C6 means that A4 is false, which once again leads us into the situation of knowing that Alice's remaining statements are true.
C4 means that B4 is false, A7 means that B5 is false. A8 means that C8 is false so C3 is true, which means that B6 is false. So Bruno has seven false statements, so the assumption that Deirdre is always correct must be false. Therefore, Alice is the one that is always correct.
Jumping back to the very beginning, this gives us the following:
| Alice | Bruno | Chester |
Deirdre | |
| Alice | ------ | | | Diary | |
| Bruno | | ------ | | | Textbook |
| Chester | | Loudspeakers | ------ | | |
| Deirdre | | | | ------ | Model train |
| Ribbon | | Water colours | Pocket watch | |
| T | A1: water colours to Chester |
| T | A2: ribbon to Alice |
| T | A3: model train from Deirdre |
| T | A4: diary from Alice |
| T | A5: diary and pocket watch to Deirdre |
| T | A6: loudspeakers from Chester to Bruno |
| T | A7: textbook from Bruno |
| T | A8: pocket knife not from Chester |
| | B1: DVD player to Alice |
| | B2: textbook to Chester |
| F | B3: diary and chocolates to Bruno |
| | B4: chocolates from Alice |
| | B5: socks from Bruno |
| | B6: DVD player from Bruno |
| F | B7: model train from Bruno |
| | B8: mittens from Alice to Bruno |
| F | C1: pocket watch to Bruno |
| F | C2: ribbon to Bruno |
| | C3: DVD player from Chester |
| F | C4: pocket watch from Alice |
| | C5: ribbon from Chester |
| F | C6: diary from Chester |
| F | C7: textbook from Chester |
| F | C8: pocket knife from Chester to Deirdre |
| | D1: socks to Alice |
| T | D2: loudspeakers to Bruno |
| | D3: DVD player to Deirdre |
| | D4: model train to Bruno |
| | D5: water colours from Deirdre to Chester |
| | D6: chocolates to Chester |
| F | D7: pocket watch to Chester |
| | D8: textbook and ribbon to Alice |
Since Chester has six false statements, the remaining two must be true. So the silk ribbon is from Chester to Alice, and the DVD player is from Chester to Deirdre (since he gave Alice the ribbon and Bruno the loudspeakers). Therefore, B1 and B6 are false, and this gives Bruno four false statements, telling us that B2, B4, B5 and B8 are true.
This gives us:
| Alice | Bruno | Chester |
Deirdre | |
| Alice | ------ | Mittens | | Diary | Chocolates |
| Bruno | | ------ | Textbook | | Socks |
| Chester | Ribbon | Loudspeakers | ------ | DVD
player | |
| Deirdre | | | | ------ | Model train |
| | | Water colours | Pocket watch | |
| T | A1: water colours to Chester |
| T | A2: ribbon to Alice |
| T | A3: model train from Deirdre |
| T | A4: diary from Alice |
| T | A5: diary and pocket watch to Deirdre |
| T | A6: loudspeakers from Chester to Bruno |
| T | A7: textbook from Bruno |
| T | A8: pocket knife not from Chester |
| F | B1: DVD player to Alice |
| T | B2: textbook to Chester |
| F | B3: diary and chocolates to Bruno |
| T | B4: chocolates from Alice |
| T | B5: socks from Bruno |
| F | B6: DVD player from Bruno |
| F | B7: model train from Bruno |
| T | B8: mittens from Alice to Bruno |
| F | C1: pocket watch to Bruno |
| F | C2: ribbon to Bruno |
| T | C3: DVD player from Chester |
| F | C4: pocket watch from Alice |
| T | C5: ribbon from Chester |
| F | C6: diary from Chester |
| F | C7: textbook from Chester |
| F | C8: pocket knife from Chester to Deirdre |
| | D1: socks to Alice |
| T | D2: loudspeakers to Bruno |
| | D3: DVD player to Deirdre |
| | D4: model train to Bruno |
| | D5: water colours from Deirdre to Chester |
| | D6: chocolates to Chester |
| F | D7: pocket watch to Chester |
| F | D8: textbook and ribbon to Alice |
As can be seen from the table, the pocket watch is from Bruno, the socks are Alice's, the box of chocolates belongs to Chester and the water colours are from Deirdre. Also, since D7 and D8 are both false, D4 has to be true, leaving only one spot for the pocket knife; from Deirdre to Alice.
